Compositions to enhance the efficacy and safety of bio-pharmaceutical drugs

ABSTRACT

Optimal ratios of pharmaceutical compositions of β-1 and β-2 agonists with their respective antagonists. Safer, more cost-effective drugs for heart and lung therapies are made by combining specific antagonists with their agonists to prevent desensitization of cellular receptors, reducing some of the unwanted side-effects of the agonist drugs alone. Determining the optimal concentration of an antagonist or inhibitor, which is necessary to prevent desensitization, without causing unnecessary and unwanted inhibition, creates a new class of pharmaceuticals. To derive an optimum ratio for a specific composition, a formulative method is provided to detail how competitive antagonists of the receptor should be combined with agonists, in specific proportions, to maximize and maintain receptor response throughout drug administration. The “optimal ratio” methodology used to determine a specific agonist/antagonist composition, to prevent β-1 or β-2 receptor desensitization, is experimentally verified and validated for specific compositions. Alteration of a specific ratio is practiced to account for the pharmacokinetic/dynamic differences between animals and humans and within human populations.

REFERENCES TO RELATED APPLICATIONS

[0001] This application is a Continuation-in-Part (CIP) of U.S. Ser. No.08/764,145, filed on Dec. 12, 1996 and on appeal before the Board ofPatent Appeals and Interferences, which is a CIP of U.S. Ser. No.08/407,911, filed on Mar. 21, 1995 and issued as U.S. Pat. No.5,597,699, which was a CIP of U.S. Ser. No. 08/188,951, filed on Jan.31, 1994, abandoned, which was a CIP of U.S. Ser. No. 07/954,865, filedon Sep. 30, 1992, abandoned.

BACKGROUND OF THE INVENTION

[0002] 1. Field of the Invention

[0003] This invention relates generally to drug compositions thatoptimize or maximize the therapeutic effects of particularreceptor-specific agonists, while concurrently preventing or, in theleast, significantly ameliorating receptor desensitization, and whichderive from the methodology of the inventor's U.S. Pat. No. 5,597,699.More particularly, the instant invention sets forth the methodologicalimprovements, and compositions, that are derived from application ofthat patent's teachings. These improvements usher in classes ofcompositions that are pharmaceutically compensated (or fitted) toharmonize with physiologies of diverse therapy recipients.

[0004] 2. Discussion of Relevant Art

[0005] An agonist is a substance/drug that has affinity for andstimulates physiologic activity at cell receptors that are normallystimulated by naturally occurring substances. As used throughout, anagonist is such a substance/drug that produces a maximal or a nearlymaximal response, whereas an antagonist or inhibitor is a substance ormolecule that produces no response, but can block the action of thedrug-agonist. A partial agonist produces a moderate response and canalso block the response of the receptor to the agonist-compound. Acompetitive antagonist is a substance that competes with the agonist forthe receptor, but produces no response. [Note: Hereinafter, thecombination of a specific agonist with a suitable antagonist orinhibitor will have one of the identifying forms of notation:agonist-antagonist or agonist/antagonist or antagonist: agonist; in suchinstances, the dash (-), slash (/) and semicolon (:) connoting thesame.]

[0006] More than twenty years ago, the idea that beta-adrenergicantagonists could be used to treat heart failure was consideredheretical although clinical data were emerging to support this viewpoint(White, D. C., Hata, J. A., Shah, A. S., Glower, D. D., Lefkowitz, R.J., and Koch, W. J., “Preservation of myocardial β-adrenergic receptorsignaling delays the development of heart failure after myocardialinfarction.” PNAS, 97: 5428-5433 (2000) and references therein).Previously it was thought that failing hearts required positiveinotropic support and that the use of beta-antagonists would depressheart function. After more than two decades, the conventional wisdom onthis point has been overturned.

[0007] In heart failure, there is a biochemical alteration of theβ-adrenergic receptor signaling system leading to the loss of cardiacinotropic reserve through β-adrenergic receptor desensitzation. It wasdemonstrated in a recent study (White, D. C., et al.) that observeddesensitization and down-regulation of β-adrenergic receptors, seen inthe failing heart, is deleterious for normal heart function (see 2 andreferences therein). In this study, paraphrasing what the authors wrote:

[0008] (1) In a rabbit model of heart failure induced by myocardialinfarction, which recapitulates the biochemical β-adrenergic receptorabnormalities seen in human heart failure, delivery of the β-adrenergicreceptor kinase ct transgene at the time of myocardial infarctionprevents the rise in β-adrenergic receptor kinase 1 activity andexpression and thereby maintains β-adrenergic receptor density andsignaling at normal levels. Rather than leading to deleterious effects,cardiac function is improved, and the development of heart failure isdelayed. These results appear to challenge the notion that dampening ofβ -adrenergic receptor signaling in the failing heart is protective, andthey may lead to novel therapeutic strategies to treat heart disease viainhibition of β-adrenergic receptor kinase 1 and preservation ofmyocardial β-adrenergic receptor function.

[0009] (2) The most promising current therapies in heart failure is theuse of β-adrenergic receptor antagonists, which presumably block thechronic activation of the β-adrenergic receptor system bynorepinephrine. β-adrenergic receptor kinase 1 up-regulation could bethe “first-response” feedback mechanism responding to the enhancedsympathetic nervous system activity because the expression ofβ-adrenergic receptor kinase 1 in the heart can be stimulated bycatecholamine exposure. An opposing hypothesis, however, is that theincrease in myocardial G protein-coupled receptor kinase (GRK) activityoften observed in the failing heart can mediate changes within theβ-adrenergic receptor system that are not protective but that rathertake part in the pathogenesis of heart failure. If such is the case,then the inhibition of β-adrenergic receptor kinase 1 might represent anovel therapeutic target in the treatment of the failing heart.

[0010] (3) To address specifically the issue of whether β-adrenergicreceptor desensitization might have maladaptive rather than adaptiveconsequences in the setting of heart failure, we have delivered apeptide inhibitor of β-adrenergic receptor kinase 1 activity via in vivointracoronary adenoviral-mediated gene delivery to the hearts of rabbitsthat have a surgically induced myocardial infarction (MI). We have shownpreviously that this model of MI in rabbits results in overt heartfailure within 3 weeks, including pleural effusions, ascites, andsignificant hemodynamic dysfunction.

[0011] (4) The conventional view of the role of sympathetic activationin heart failure is that the resultant elevated myocardial β-adrenergicreceptor kinase 1 levels and β-adrenergic receptor desensitization inthe dysfunctional heart are actually protective mechanisms. Abrogationof such compensatory mechanisms, it has been reasoned, would only worsenthe physiologic deterioration caused by excess catecholaminestimulation. Indeed, the chronic use of β-agonists in heart failure isharmful.

[0012] (5) First, administration of an oral β-agonist leads to furtherβ-adrenergic receptor down-regulation in the lymphocytes of patientswith heart failure. Additionally, the β -adrenergic receptor kinase 1expression is increased after β-adrenergic receptor stimulation.Therefore, the use of β-agonists in heart failure patients exacerbatesdisturbances in the myocardial β-adrenergic receptor system, leading tofurther receptor down-regulation and increases in β-adrenergic receptorkinase 1. In contrast, restoration of β-adrenergic receptor signalingthrough gene delivery of the β-adrenergic receptor kinase ct has afundamentally opposite effect at a molecular level, i.e., it preservesthe number of β-adrenergic receptors and inhibits β-adrenergic receptorkinase 1. [end paraphrasing]

[0013] It is interesting that β-adrenergic receptor kinase 1 inhibitionshares with β-blockade the potential to normalize or remodel signalingthrough the cardiac β-adrenergic receptor system in heart failure.Moreover, both treatments lower cardiac GRK activity, enhancecatecholamine sensitivity, and raise or preserve myocardial levels ofβ-adrenergic receptors (White, et al. and included references). Thus, itis possible that part of the salutary effects of β-blockers on thefailing heart is because of their demonstrated ability to reduceexpression of β-adrenergic receptor kinase 1 in the heart. With theoverwhelming positive data showing the beneficial effects of β-blockersin the treatment of heart failure, it is reasonable to question whetherthe strategy of adding a β-adrenergic receptor kinase 1 inhibitor addsanything novel to the therapeutic armamentarium. However, given theresults of this study, it is apparent that β-antagonist therapy and β-adrenergic receptor kinase 1 inhibition may in fact be complementarytherapeutic modalities. [See SUMMARY OF THE INVENTION]

[0014] Present theories of receptor activation calculate the response ofa receptor as some function of an agonist-receptor complex. There havebeen several modifications and criticisms of receptor theory (see, forexample Keen, M.; Testing Models of agonist for G-Protein CoupledReceptors: Trends Pharmacol. Sci. 12, 371-374, 1991), but none of thesetreatments examined the discrete change induced by ligand binding to twoequilibrium states of a receptor and, consequently, no one has developedthe instant (and exacting) method for determining actual drugcompositions based upon an optimal ratio of agonist to antagonist whicheffectively prevent desensitization of cellular receptors that arenormally and incipiently responsive to a host of agonists. Carefulexperimental investigations of several different receptor systems haverevealed that receptor theory fails to describe the observed responsesin a number of cases. Also, the phenomenon of rapid desensitization hasbeen difficult to model by modem receptor theories. Originally many ofthese experimental observations were reported in 1957 by del Castilloand Katz in their pioneering work on desensitization (del Castillo, J.and Katz, B. Proc. Roy. Soc. Lond. 146, 369-381, 1957). The presenttheories are inadequate for at least two fundamental reasons; first,they fail to describe relevant experimental observations, except forlimited cases and second, they offer only a “black box” descriptioninstead of a physicochemical explanation for receptor response.

[0015] In 1991, Geoffrey et al. found that competitive antagonists of aglutamate receptor decreased the desensitization of the receptor (SeeGeoffrey, M., et al. Molecular Pharmacology 39, 587-591; 1991). Theyconcluded, in this study, that such paradoxical behavior could not bedescribed by the current theories of pharmacologic action deriving from(for example) experimental observations first recorded in 1957 by delCastillo & Katz performing their pioneering work on desensitization.Until most recently, no theory has been able to adequately explain howthe behavior observed by Geoffrey et al. occurs; and, the utility ofmixing competitive antagonists (or partial agonists) with agonistsaccurately and, therefore, efficiently to prevent receptordesensitization has been all but overlooked.

[0016] Other articles that show the utility (in vivo) of usingantagonist/agonist compositions, to prevent receptor desensitization,are extant. One such article is “Antitacyphylactic Effects ofProgesterone and Oxytocin on Term Human Myometrial Contractile ActivityIn Vitro” by Xin Fu, MD, Masoumeh Rezapour, MD, Mats Löfgren, MD, PhD,Ulf ulmsten, MD, PhD, and Torbjörn Bäckström, MD, PhD, all of theDepartment of Gynecology and Obstetrics, University Hospital, Uppsala,Sweden and published in Obstetrics & Gynecology (1993; 82: 532-8).Therein, Xin Fu et al. conclude that a quantum of an antagonist,progesterone, is observed to reverse the tachyphylaxis (desensitization)to oxytocin (agonist) of human myometrium. A method for quantifying thecompounds for this phenomenon is not suggested, particularly forarriving at proper dosages of the antagonist, for consistently achievingthe reversal. Nor for that matter, do Xin Fu et al. provide formulasthat will maintain a maximal receptor response.

[0017] Another disclosure is of certain importance in the quest for invivo studies to support modeling investigational techniques in drugresearch: “Beta1 and Beta2 Adrenoceptors in the Human Heart: Properties,Function, and Alterations in Chronic Heart Failure” by Otto-Erich Bröddeof Bio-chemisches Forschungslabor, Medizinische Klinik and Poliklinik,Abteilung für Nieren-und Hochdruckkrankheiten, Universitätsklinikum,Essen, Germany. (Pharmacological Review, 1991, Vol. 43, No. 2). This isa detailed study on chronic heart failure which discusses a recognizedutility of using Beta-AR (beta-adrenergic receptor) antagonists forpatients in certain types of heart failure (pp. 228-230) and whichhypothesizes that such work by occupying Beta-ARs and preventdesensitization of cardiac Beta-ARs (see p. 233 and references therein).[NOTE: No further information is detailed which would inform one ofordinary skill how to quantify the portions of antagonists necessary tofully retard i.e., prevent “down-regulation” (desensitization, ibid p.233) of Beta-ARs.]

[0018] As recently as Jul. 24, 1994, the instant inventor presented hiswork “A Novel Biophysical Model for Receptor Activation” (R. Lanzara,CUNY, New York and Bio-Balance, Inc., New York, N.Y.) to the XIIthInternational Congress of Pharmacology at Montréal, Québec, Canada Alsopresented was a paper published by him concerning Weber's Law (“Weber'sLaw Modeled by the Mathematical Description of a Beam Balance”,Mathematical Biosciences, 122:89-94 (1994)). These works are includedfor their teachings on the instant concept, methods of calculation toprovide quanta of antagonist: agonist necessary for achieving theobjectives of the invention and demonstrate objectively by use of invivo empirical studies that the invention is a substantial improvementto the prior art and a significant advancement in the field.

INCORPORATION BY REFERENCE

[0019] The following of the aforementioned works: Geoffroy et al.“Reduction of Desensitization of a Glutamate Ionotropic Receptor byAntagonists” Molecular Pharmacology 39: 587-91 (1991); Xin Fu et al.,“Antitachyphylactic Effects of Progesterone and Oxytocin on Term HumanMyometrial Contractile Activity In Vitro”, Obstetrics & Gynecology, 82:532-38 (1993); OttoErich Brodde, “Beta1 and Beta2 Adrenoceptors in theHuman Heart: Properties, Function, and Alterations in Chronic HeartFailure”, Pharmocological Review, Vol. 43, No. 2 (1991); Lanzara, R. “ANovel Bio-physical Model for Receptor Activation” Dept. of Allied HealthSci., CUNY, NY, N.Y. and Bio-Balance Inc., NY, N.Y.; and, Lanzara, R.“Weber's Law Modeled by the Mathematical Description of a Beam Balance”,Mathematical Biosciences, 122: 89-94 (1994) are incorporated herein byreference.

SUMMARY OF THE INVENTION

[0020] The problem is solved for determining the optimal ratio for theconcentration of an antagonist- or inhibitor-to-agonist which issufficient to prevent cellular receptor desensitization, and, withoutcausing unnecessary and unwanted inhibition, maintaining a maximalresponse. The instant, improved method and formulas describe not only f,the concentration of the antagonist relative to that of the agonist(given by K_(i), the dissociation constant of the antagonist, divided byφ, the square root of one-half of the product of the two dissociationconstants of the drug-agonist for the receptor), but provide amethodology for obtaining the various formulary factors by which Iderive the specific ratios of the selected agonist and antagonist forreceptor classes among the diverse animal species. When higher ratios ofthe antagonist are used, more inhibition of the response occurs; andwhen lower ratios are used, desensitization results.

[0021] It is noted that, in the relevant art, there exists a method forcalculating drug efficacy by utilization of easily identifiablebiophysical parameters. Additional to both in vitro and in vivo datagleaned from the incorporated references (Xin Fu, et al. and Otto-ErichBrodde, ibid.), I initially had performed an in vitro test on Guinea pigtrachea, a widely used substitute tissue for pharmacologic research onhuman trachea, to determine the optimal composition of an antagonist(propranolol) which is mixed with an agonist (isoproterenol) in order toprevent receptor desensitization produced by a large concentration ofsaid agonist (isoproterenol=25 μM). Specifically, the experimental dataand the calculated values were compared. The agreement of theexperimental data with the calculated value for f=K_(i)/φ was within oneand one-quarter percent (1.25%; calculated=0.0395 vs.experimental=0.04). This excellent result validated the method forcalculating the optimal ratio of the agonist/antagonist compositions toprevent receptor desensitization. This was a specific test of thisinvention to determine the optimal ratio of propranolol to isoproterenolin the Guinea pig trachea and proved that there exists a maximallyeffective ratio that finds utility in its ability to preventagonist-induced drug desensitization.

[0022] The instant method of preventing β-adrenergic receptordesensitization or down-regulation, by creating the optimal ratio ofagonist to antagonist combinations, is a complementary therapeuticstrategy to what the recent study ( White, D. C. et al., ibid.) suggestsas an appropriate therapy to maintain β-adrenergic receptor signaling inpatients with heart failure. The difference between our approaches isthat while the authors of this study advocate the delivery of anintracellular inhibitor of the β-adrenergic receptor kinase through the“β-adrenergic receptor kinase ct transgene”, I advocate that, by theproper titration of agonist to antagonist, the same beneficial effectswill occur. Many of these effects were mentioned by these authors asresulting from both β-blockade therapy and their own “transgenetherapy”. The instant teaching is that, because the endogenous levels ofcatecholamines are usually elevated in patients with heart failure,concomitant use of β-blockers reduces the desensitization of thesereceptors in these patients with higher than normal norepinephrine orepinephrine levels. This can be more easily understood by observing thatin FIG. 2 of my 1997 patent (Lanzara '699, ibid.), the use of anyinhibitors (β-blockers) will improve the relative response for thedesensitized portion of the curve (to the right of the peak). Therefore,the Lanzara compositions represent the best mode of practice to maintainthe β-adrenergic signaling in the failing myocardium.

[0023] Having been encouraged by initial successes, I have been able tocompound a host of pharmaceuticals that are the scientifically derivedoptimal ratios, i.e., agonist-antagonist, that work best for the largestpopulation, yet have the least side-effect impact. More to the lattercharacteristic, I have found, through further empirical studies that,relative to heart therapies, the invention's new compositions presentedwith significantly less arrhythmias than did agonists alone. A specificcomposition comprising isoproterenol with metoprolol in the ratio of1:85, Iso:Met, comprising for a single microgram amount of isoproterenolHCl, 85 micrograms of metoprolol tartrate, is used as a safer and moreefficacious alternative to isoproterenol alone. I alter this ratio in amanner normally practiced in the pharmaceutical industry to account forthe pharmacokinetic and pharmacodynamic differences between animals andhumans and within populations.

BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Of the drawings:

[0025]FIG. 1 depicts ligand equilibria with the ionic forms of thereceptor;

[0026]FIG. 2 is a graphical representation of Relative Response vs.Concentration for Different Concentrations of the Competitive Inhibitor,[I];

[0027]FIG. 3 reflects curves for the responses as determined byStephenson;

[0028]FIG. 4 is a model of ΔRH to the operational model and the data ofKeen;

[0029]FIG. 5 is the response curves of Dilger and Brett modeled by ΔRHwith a diffusion equation;

[0030]FIG. 6 is an experimental dual plot modeling: del Castillo andKatz dose-responses;

[0031]FIG. 7 presents empirical data obtained for in-vitro studies oncarbachol-contracted Guinea pig trachea;

[0032]FIG. 8 is a graphical fit of the calculated data (Δ-delta) to theexperimental data (dP/dt) for the agonist (isoproterenol), with andwithout a fixed amount of the antagonist (metoprolol);

[0033]FIG. 9 is a plot of the experimental response in the test animalsto the calculated optimal ratio of agonist/antagonist (Iso/MetCombination) derived from the biophysical parameters obtained fromfitting the test dosages in FIG. 8 to the equations 6-10;

[0034]FIG. 10 is a graphical comparison of the experimental dP/dt inrats for dobutamine alone (Dob) versus the optimal ratio combination ofdobutamine/metoprolol (Dob+Met);

[0035]FIG. 11 is a graphical comparison of the fit of theory (Δ-delta)to the experimental results (dP/dt normalized and Experiment Iso/MetCombination) in vivo.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

[0036] For all of the known receptors, most experimental observationshave shown that agonist ligands display two-site binding whileantagonist ligands display one-site binding. The experimentalobservations can be understood as a preferential binding of the agonistsfor one form of the receptor. This gives rise to the observed two-sitebinding and the two dissociation constants of the drug for the receptor.This is demonstrated to be a direct consequence of the efficacy of theagonist and is a measure of the response of the system. By thisreasoning, antagonists would display equal or nearly equal affinitiesfor each form of the receptor. This is observed as one-site binding anda single dissociation constant for antagonist binding to receptors. Fora receptor that exists in two states, an ionizable receptor was selectedas a likely example because there is experimental evidence to supportthis. (See: Davies, A. O. J. Clinical Endocrinology & Metabolism 59,398-405 (1984); Gende, O. A., Hurtado, M. C. C. & Cingolani, H. E. ActaPhysiol. Pharmacol. Latinoam. 35, 205-216 (1985); Hall, M. D., et al.Neurochemical Research 11, 891-912 (1986); Asselin, J., et al. Biochem.J. 216, 11-19 (1983); Barlow, R. B. & Hamilton, J. T. Brit. J. Pharmacol18, 543-549 (1962); Battaglia, G., Shannon, M., Borgundvaag, B. andTiteler, M. Life Sciences 33, 2011-2016 (1983); and Rocha E. Silva, M.Arch. Int. Pharmacodyn. 128, 355-374 (1960)).

[0037] In FIG. 1, the equilibria of the ligand with the ionic forms ofthe receptor are shown. The two free forms of the receptor (R_(H) andR_(L)) which can exist in either an ionized (R_(H)) form or anon-ionized (R_(L)) form, respectively, react with the drug D, with twodifferent dissociation constants, K_(DH) and D_(DL); DR_(H) and DR_(L)are the amounts of the drug-receptor complex in either the high affinityor low affinity forms, respectively. The drug-receptor complex can alsoexist in either an ionized (DR_(H)) form or non-ionized (DR_(L)) form.The non-ionized form is the lower affinity form. This characterizationteaches that the protonation of at least one (class of) residue withinthe receptor alters the affinity of the drug for the two free states ofthe receptor. The K_(R) term is the dissociation constant of thehydrogen ion (H⁺) binding to the receptor in the absence of the drug.The K_(RD) term is the dissociation constant of hydrogen ion (H⁺)binding to the receptor in the presence of the drug.

[0038] The drug (or ligand) binding to each of the two receptor statescan be described by the Langmuir binding expressions:

DR _(H) =R _(H)(D)/((D)+K_(DH)) and DR _(L)=R_(L)(D)/((D)+K _(DL))

[0039] where DR_(H) and DR_(L) are the amounts of the drug-receptorcomplex for the high and low affinity states, respectively; and, R_(H)and R_(L) are the total amounts of the receptors in the high and lowaffinity states. The ligand will have a preference for binding to thehigh affinity receptor state, R_(H), over the low affinity receptorstate, R_(L), which is a direct result of the different dissociationconstants K_(DH) and K_(DL). Any differences in the affinities of aligand for the two receptor states produces a “shift” in the receptorreaction quotient similar to Le Chatelier's Principle.

[0040] Now introducing a new term, Γ, as a ratio of the high affinitystates of the receptor to the low affinity states, the followingexpression is obtained:

Γ=(R _(H) +DR _(H))/(R _(L) +DR _(L))  [1]

[0041] where Γ is a “weighted ratio” of the two receptor states. Bysubstituting the binding expressions for DR_(H) and DR_(L) the completeexpression for Γ can be described as:

Γ=R _(H)(1+(D/(D+K _(DH))))/R _(L)(1+(D/(D+K _(DL))))  [2]

[0042] The derivation of equation [2] includes the assumption that theconcentrations of the free receptor states (R_(H) and R_(L)) aredetermined by the environmental influences on the protonation anddeprotonation of the receptor and that the drug binding to each statecan be described by Langmuir binding. Perhaps the closest physicalanalogy to elucidate this “weighted ratio” approach is that the receptorequilibrium may be considered analogous to a beam balance with weights.The addition of a ligand is comparable to the addition of weights toeach side of the balance relative to a hypothetical affinity with oneside having the more weight or “higher affinity”. The weighted ratiowould be the ratio of the original weight plus the additional weight onthe “high affinity” side of the fulcrum divided by the original weightplus the additional weight on the “low affinity” side. Additionally, asecond weighted ratio would be the distances of the centers of mass fromthe fulcrum. This second weighted ratio would comprise the originaldistances plus or minus the change in these distances that was necessaryto maintain the horizontal equilibrium point. The two weighted ratioswill be equivalent and similar to this analysis of the receptorresponse. Similarly a second or parallel determination of Γ can be madefrom consideration of the conservation of matter law. This requires thatany discrete change or increase (+x) in the high affinity state must bereciprocated by an equal and opposite change (−x) in the low affinitystate with all receptor states equal to the total number of receptors(R_(T)). In this case, the equation for mass balance can be expressedas:

R _(T)=(R _(H) +x)+(R _(L) −x)  [3]

[0043] Therefore, the weighted ratio of the high to low affinity statescan be alternatively expressed as:

Γ =(R _(H) +x)/(R _(L) −x)  [4]

[0044] and Equation [4] can be solved for the discrete change, x, whichyields:

x=(ΓR _(L) −R _(H))/(1+Γ)  [5]

[0045] The equivalence of equations [1] and [4] was tested numerically(not shown); also the expression for Γ from equation [1] can besubstituted into equation [5] and subsequently into equation [4] toproduce the original expression for Γ. Equating the weighted ratios ofthe high and low affinity receptor states in terms of the ligand bindingor the conservation of matter law does not appear to have been donebefore. Equating the two weighted ratios, equations [2] and [4], andsolving for x yields: $\begin{matrix}{{\Delta \quad {RH}} = \frac{R_{H}{R_{L}(D)}\quad \left( {K_{DL} - K_{DH}} \right)}{{{R_{L}\left( {{2D} + K_{DL}} \right)}\quad \left( {D + K_{DH}} \right)} + {{R_{H}\left( {D + K_{DL}} \right)}\quad \left( {{2D} + K_{DH}} \right)}}} & \lbrack 6\rbrack\end{matrix}$

[0046] where ΔR_(H) is substituted for x, in order to emphasize that itrepresents the change in the high affinity state.

[0047] Taking the first derivative of the above equation with respect tothe dose, D, and setting it equal to zero in order to obtain the peak(maximum) curve yields the following expression for the concentration ofthe drug where this peak occurs:

D=(K _(DH) K _(DL)/2)^(½)  [7]

[0048] In the presence of an antagonist or inhibitor (I), theequilibrium constants, K_(DH) and K_(DL), will each be multiplied by(K_(i)+[I])/K_(i) so that equation (7) becomes:

D=(K _(DH) K _(DL)/2)^(½)(K _(i) +[I])/K _(i)  [8]

[0049] If the concentration of the inhibitor (I) is expressed as afraction (f) of the dose of the drug D, i.e., [I] =f[D], thensubstitution of this expression for [I] into equation (8) and solvingfor f yields:

f=K _(i)(D−φ)/φD  [9]

[0050] where,

φ=(K _(DH) K _(DL)/2)^(½)

[0051] Observing that equation (9) gives the minimal fractionalconcentration of the inhibitor with respect to the drug that isnecessary to prevent the desensitization of the receptor, it followsthat as [D] becomes much larger than φ, equation (9) becomes:

f=K _(i)/φ  [10]

[0052] This is the fractional dose of the antagonist relative to theconcentration of the agonist or drug which is necessary and sufficientto prevent any desensitization of the receptor for the particular drugthat is being used. This is refered to as the optimal ratio for anyagonist-antagonist composition.

[0053] The instant formulation determines the lowest acceptable dose ofinhibitor or antagonist to mix with the drug which completely preventsdesensitization. It expresses the dose of inhibitor as a fraction of thedose of the drug. Further, the formulation prevents significantinhibition of the response at lower concentrations of the drug, yetprevents any of the desensitization of the receptor which is a directresult of the high concentrations of the drug (see FIG. 2).

[0054] Referring particularly to FIG. 2 there is shown a graphicaldemonstration of the ability of the formulation f D=I to preventdesensitization without affecting the maximum response. Experimentally,computer simulations were carried out to demonstrate the ability of thismodel, equation [6], to describe a number of dose-response curves thatwere difficult or impossible to model by previous theories. Previouslypublished experiments were compared to the predictions from this model.As an example, the experimental dose-response curves from del Castilloand Katz were described by equation (6) with and without an inhibitor(see FIG. 6).

[0055] Other experimentally determined curves have been described by mymethod including the more recent work of Keen (Keen, M., TrendsPharmacol. Sci. 12, 371-374 (1991)). The response curves from Keen aregiven in FIG. 4, wherein the darker curves are the computer generatedcurves from the model and fit those curves from the experiments and,whereas the lighter curves (generated from the prevalent operationalmodel) failed to fit the experimental curves. Examples followhereinafter in more detail, illustrative of the experimental developmentof my invention.

EXAMPLE 1

[0056] Stephenson's data (Stephenson, R. P., British. J. Pharmacol. 11,379-393 (1956)) are presented in FIG. 3. The points on these curves weregenerated by equation [6]. The value for both of the R_(H) and R_(L)terms was 50 and the values of the pairs of K_(DH) and K_(DL) terms wereas follows: Butyl (3×10⁻⁶, 8×10⁻²); Hexyl (5×10⁻⁶, 2×10⁻³); Ethyl(1×10⁻⁴, 1×10¹); Heptyl (2×10⁻⁵, 3×10⁻⁴); Octyl (3×10⁻⁵, 2×10⁻⁴) ; Nonyl(4×10⁻⁵, 2×10⁻⁴); and Decyl (3×10⁻⁵, 2×10⁻⁴). The concentration of drug[D] is represented on the abscissa in a molar log scale.

[0057] The reader will note that equation [6] can represent theexperimental data from Stephenson with meaningful biophysical parameters(i.e. the two dissociation constants of the drugs for the two receptorstates).

EXAMPLE 2

[0058] Referring once again to FIG. 4, the plots of ΔR_(H) (equation[6]−solid lines) for the data of Keen (Keen, 1991) are presented forarecoline, pilocarpine and carbachol as well as the plots of theoperational model (broken lines). ΔR_(H) was calculated with 300 as thevalue for the R_(H) and R_(L) terms to scale the curves appropriately.The K_(DH) and K_(DL) terms were varied in order to model theexperimental curves. The K_(DH) and K_(DL) values for arecoline were 2and 2000 respectively; similarly, the values for pilocarpine were 4 and220; and the values for carbachol were 0.02 and 1000.

[0059] The equation to calculate the curves for the operational model:${\% \quad {response}} = \frac{\alpha \quad \left( {\left\lbrack R_{O} \right\rbrack/K_{AR}} \right)\quad \left( {D/K_{A}} \right)}{1 + {\left( {1 + \left( {\left\lbrack R_{O} \right\rbrack/K_{AR}} \right)} \right)\quad \left( {D/K_{A}} \right)}}$

[0060] where ([R_(O)]/K_(AR))=16, 7.3, 3.5, 1.3 and 0.116 with α=100%(plotted as the broken lines in the graph). KA is the overalldissociation constant for the binding of the agonist to the receptor asdefined in the operational model.

[0061] Experimentally determined response curves were examined to testthe ability of ΔRH to model these curves. The experimentally determineddose-response curves from Keen (Keen, 1991) and Stephenson (Stephenson,1956) were easily modeled by ΔRH from equation [6] with appropriatelyselected K_(DL) and K_(DH) values (FIGS. 3 and 4). Although there may besome tissue dependent effects from unstirred layers or diffusionbarriers, no modifications were used in order to model these curves.Other curves were examined to test the ability of equation [6] to modelthese curves and to determine additional factors that may be necessaryto model the total response.

[0062] Basically, there were two modifications to ΔRH that werenecessary to model the experimental dose-response curves of Dilger andBrett (Dilger, J. P. and Brett, R. S., Biophysical J. 57, 723-731,(1990)) and del Castillo and Katz. The first modification was adiffusion equation to model the time-dependence of the ligandconcentration at the receptors and the second modification was a“recruitment function” to model the concentration-dependent “diffusionalrecruitment” of additional receptors.

[0063] Most experimental preparations have multiple diffusion barriersor unstirred layers in the preparations which can cause time-dependentchanges in the agonist concentration at the receptor sites. In order toaccount for this, the following diffusion equation was used:${\lbrack D\rbrack \quad t} = \frac{{(D)10^{({t^{*}{Q/{r2}}})}} - (D)}{10^{\quad {({t^{*}{Q/{r2}}})}}}$

[0064] where [D]t is the time-dependent change in agonist concentration.(D) is the applied concentration of the agonist; “t” is the time; “Q” isthe diffusion coefficient of the agonist and “r” is the estimatedaverage diffusion distance. With [D]t substituted for (D) in equation[6], a time-dependent response could be modeled. The diffusionexpression appears necessary to describe a time-dependence to theexperimental curves, but not the overall shapes of these curves.

[0065] Because the peak heights of some experimental curves vary withthe applied dose of agonist, an additional modification to ΔRH wasnecessary to model these curves. Application of high agonistconcentrations produce large peaks, whereas, lower agonistconcentrations produce small peaks in the measured dose-response curves.This is not predicted from plots of ΔRH with or without a diffusionequation. One explanation for this phenomenon is that there is aconcentration-dependent “diffusional recruitment” of receptors. Katz andThesleff (Katz, B. and Thesleff, S., J. Physiol. 138, 63-80 (1957)) andmore recently Cachelin and Colquhoun (Cachelin, A. B. and Colquhoun, D.,J. Physiol.415, 159-188, (1989)) suggested that agonists may diffuse todistant receptors in their preparations and they proposed aconcentration-dependent change in the total number of receptors as anecessary modification. The receptors which do not participate in theresponse at low agonist concentration may be either physically distantor separated by diffusion barriers within a particular preparation. Thissuggests that some of the receptors are removed from the initial site ofagonist exposure but become “recruited” as the concentration of theagonist is increased. Because the experimental curves from Dilger andBrett have decreasing peak heights with decreasing agonistconcentrations, a “recruitment function” was found necessary to modifyΔRH. This “diffusional recruitment” can be modeled approximately by ahyperbolic function which includes the ligand concentration and anapparent dissociation constant for the half maximal receptorrecruitment. $R_{F} = \frac{R_{M}(D)}{(D) + {KF}}$

[0066] where R_(M) represents the relative maximum number of receptorsand K_(F) is the apparent dissociation constant for the concentration ofacetylcholine which produces a half maximum of the peak height. R_(F)adjusted the relative number of receptors contributing to the totalresponse by multiplying ΔRH times R_(F).

EXAMPLE 3

[0067] As depicted in FIG. 5, the response curves of Dilger and Brettare modeled by ΔRH with a diffusion equation, [D]t, to represent thechange in concentration with time and a recruitment function, R_(F), todescribe the diffusional recruitment of receptors. The diffusioncoefficient used for acetylcholine (ACH) is 6×10−10 m2s−1, which is agenerally accepted value. The values for the R_(H) and R_(L) terms areone for this graph. The apparent affinity constant for the diffusionalrecruitment of receptors, K_(F), is 20 μM as determined by the halfmaximal change in the peak heights of the experimental curves. Where “t”is the time in seconds and “900×10-12” is the square of the distance(30×10-6 m). The K_(DH) and K_(DL) values of acetylcholine are 0.01 and0.1 respectively.

[0068] The series of equations to calculate ΔRH are:$R_{F} = {{100\quad {D/{\left( {D + K_{F}} \right)\lbrack D\rbrack}}t} = \frac{{(D){10\quad}^{({t^{*}6 \times {10/900} \times 10})}} - (D)}{{10\quad}^{({t^{*}6 \times {10/900} \times 10})}}}$${DR}_{H} = \frac{{R_{H}\lbrack D\rbrack}t}{{\lbrack D\rbrack t} + K_{DH}}$${DR}_{L} = \frac{{R_{L}\lbrack D\rbrack}t}{{\lbrack D\rbrack t} + K_{DL}}$$\Gamma = \frac{R_{H} + {DR}_{H}}{R_{L} + {DR}_{L}}$${\Delta \quad {RH}} = \frac{R_{F}\left( {{\Gamma \quad R_{L}} - R_{H}} \right)}{1 + \Gamma}$

[0069] where the last four equations are operationally equivalent toequation [6] for ΔRH. The effect of a competitive inhibitor on theresponse curves can be modeled by including the expressions forcompetitive inhibition into the Langmuir binding expressions for DR_(H)and DR_(L) and then substituted into equation [5], so that the weightedratio becomes:$\Gamma = \frac{R_{H}\left( {1 + \left( {D/\left( {D + {K_{DH}\left( {1 + {I/K_{i}}} \right)}} \right)} \right)} \right)}{R_{L}\left( {1 + \left( {D/\left( {D + {K_{DL}\left( {1 + {I/K_{i}}} \right)}} \right)} \right)} \right)}$

[0070] where “I/K_(i)” is the concentration of the inhibitor divided bythe dissociation constant of the inhibitor for the receptor. The effectof an antagonist or competitive inhibitor on the response curve showsthat when the inhibitor is present the slope of the response curve onthe descending side diminishes more than the slope on the ascending sideof the curve which is similar to the experimental observations of delCastillo and Katz as well as Geofroy et al.

EXAMPLE 4

[0071]FIG. 6 consists in the two plots of ΔRH which model theexperimental dose-response curves of del Castillo and Katz. ΔRH iscomputed by the series of sequential equations shown below. The valuesfor the R_(H) and R_(L) terms are 100. The initially appliedconcentration of acetylcholine (ACH) was 100 μM. The values for themaximum peak response of acetylcholine (100 μM) and half maximal peakresponse (20 μM) were taken from Dilger and Brett for use in therecruitment function, R_(F). The effective diffusion distance in [D]t is191 μm and “t” is the time in seconds which is converted tomilli-seconds for the plot. The inhibitor concentration fordecamethonium, expressed as I/K_(i) is equal to either 0 or 1([I]=K_(i)) for the two plots. The recruitment function, R_(F), alsoincludes the effect of the competitive inhibitor. Decamethonium, whichwas a weak partial agonist in the hands of del Castillo and Katz, istreated as a competitive antagonist without any contribution to theresponse.

[0072] The series of equations to calculate ΔRH:$R_{F} = {{{\frac{200\quad (D)}{(D) + {K_{F}\left( {1 + {I/K_{i}}} \right)}}\lbrack D\rbrack}\quad t} = \frac{{(D)10^{({t^{*}6 \times {10/364} \times 10})}} - D}{10^{({t^{*}6 \times {10/364} \times 10})}}}$${DR}_{H} = \frac{{R_{H}\lbrack D\rbrack}t}{{\lbrack D\rbrack t} + {K_{DH}\left( {1 + {I/K_{i}}} \right.}}$${DR}_{L} = \frac{{R_{L}\lbrack D\rbrack}t}{{\lbrack D\rbrack t} + {K_{DL}\left( {1 + {I/K_{i}}} \right)}}$$\Gamma \quad = \frac{R_{H} + {DR}_{H}}{R_{L} + {DR}_{L}}$${\Delta \quad {RH}} = \frac{R_{F}\left( {{\Gamma \quad R_{L}} - R_{H}} \right)}{{1 + \Gamma}\quad}$

[0073] To apply the instant methodology to a specific case requiringadministration of a drug to a human subject according to a commonlyaccepted protocol (state of the art), one first obtains the drug'sdose-response curve that is provided by the drug's maker or areexperimentally determined. The curve is then “fitted” by normalizing forthe total number of receptors and optimizing the values for the high andlow affinity constants K_(DH) and K_(DL). These fitted values are theentering biophysical arguments for the calculation of φ and f, accordingto this specification, which results in the optimal ratio of theantagonist with respect to the drug-agonist (antagonist: agonist) thatis necessary to prevent desensitization of the receptor. Theadministration of antagonist is by normal delivery methods of its owncharacter and may be done during the agonist administration or, if suchis autonomic in the recipient, concurrent therewith, or shortlythereafter. Agonists and antagonists are made into pharmaceuticalcompositions by combinations with appropriate medical carriers ordiluents. For example, such mixtures can be dissolved in oils, propyleneglycol, physiological saline, isopropyl myristate, ethanol, cremophor,glycol, sesame oil, or other such pharmacological solutions. Formulationas topicals is also available. Pharmacologists familiar with the panoplyof drugs and their professional literature may readily use the inventionwith the guidance herein provided.

[0074] As a result of numerous in vivo studies and my biophysicalmodels, several antagonist/agonist pairings of any of the possiblecombinations of a beta-1-agonist with any of the possiblebeta-1-antagonists (or partial agonists), in the ratios taught herein,include without limitation: isoproterenol/acebutalol;isoproterenol/atenolol; isoproterenol/labetalol;isoproterenol/metoprolol; isoproterenol/nadolol;isoproterenol/oxprenolol; isoproterenol/pindolol;isoproterenol/propranolol; isoproterenol/sotalol; andisoproterenol/timolol. Similar compositions are made for each of thefollowing beta-1-agonists: adrenaline; dobutamine; epinephrine;ephedrine; metaproteronol; norepinephrine; noradrenaline; and xamoterol,for example: dobutamine/propranolol; dobutamine/atenolol;dobutamine/betaxolol; dobutamine/metoprolol; dobutamine/timolol;dobutamine/sotalol; dobutamine/pindolol; dobutamine/betaxolol;norepinephrine/atenolol ; ephedrine/timolol; epinephrine/sotalol;noradrenaline/pindolol; xamoterol/betaxolol; andmetaproteronol/propanolol, to name but a few suchbeta-1-agonist/antagonist combinations. The invented compositionsinclude all drugs or molecular entities capable of acting as eitherbeta-1-antagonists or beta-1-agonists as the molecular entities to beused in making these compositions; and they also include the use of theenantiomers of the beta-1-antagonists and beta-1-agonists as the workingmolecular entities.

[0075] Initial Experiment

[0076]FIG. 7 provides in vitro experimental data (CEREP, CELLEL=EVESCAULT, France rpt. No. 1124 R 820E), which verify my “optimalratio method” to determine a specific agonist/antagonist composition toprevent β2 receptor desensitization. The inhibitor constant K_(i), wasfirst determined for two concentrations of propranolol (1.0 μM and 10.0μM) measured on the desensitized preparations. The value for K_(i) was2.96× 10⁻⁷ M. This low value is reasonable because the tissues weretreated with 30 μM of the catechol-O-methyl transferase inhibitor U-0521which was added for forty-five minutes prior to exposure toisoproterenol (the agonist) or propranolol (the antagonist) and presentthereafter. This “blunting” of the K_(i) has been previously observed inthe presence of metabolic inhibitors. The value of the maximum of thecontrol curve was calculated from a fit of the curve as previouslydescribed in this disclosure. This value was calculated fromφ=(K_(DL)K_(DH)/2)^(−½)and found to be 7.48×10⁻⁶ M. It also agreed witha measured estimate from the experimental points. In order to calculatethe fraction of inhibitor necessary to prevent receptor desensitization,the following was calculated: f=K_(i)/φ and found to be 3.95×10⁻² whichis in excellent agreement with the experimentally determined values of1.0 μM propranolol/25.0 μM isoproterenol which gives f=0.04. Thus, thisexperiment confirmed the preparation of an optimal ratio made accordingto the herein disclosed method. In determining the optimal ratio ofpropranolol to isoproterenol in order to prevent theisoproterenol-induced desensitization in the Guinea pig isolatedtrachea, it was noted that other concentrations of propranolol (0.2 and10.0 μM) that were tested experimentally, were found to be ineffectivein restoring the maximum response of the tissue. These results provevalid my initial hypothesis, and later assertion, that there is amaximally effective ratio which will provide the intended results sincethe concentrations of the propranolol were either smaller or larger thanthe 1.0 μM found to be optimal for this system.

[0077] The conclusions garnered from this specific test show that theinvention is logically extendable to include other agonist-antagonistpairs on other receptors which display desensitization or fade. Sincepropranolol has been labeled as a “negative antagonist” or an “inverseagonist”, those ligands labeled as negative antagonists or inverseagonists would be included in the term “antagonists” within the meaningof this disclosure. Additionally, these compositions can be seen toreverse previously desensitized receptors. The logical extensibility ofmy invention to include other agonist-antagonist pairs on otherreceptors and the fact that these compositions can reverse previouslydesensitized receptors are further militated by a detailed reading ofthe incorporated references which, although not anticipatory orsuggestive of the instant methods and compositions, nonetheless providedata which may be analyzed to infer confirmation of my teachings.

[0078] Experiments for Cardiac Desensitization

[0079] There was made a fit of the experimental data for the agonist(showing the expected desensitization) with and without the antagonist(at a fixed concentration) to the theory (Δ or ΔRH from equations 1-10.Referring to the first graph, FIG. 8, labeled “Rat Heart”, this wascreated by fitting the experimental data for the isoproterenol (Iso)alone to the equations 1-10. This was done both with and without a fixedamount of metoprolol (Met) (1 mg/kg/min) to determine the K_(i) for theantagonist, Met. The experimental points for Iso alone are labeled“dP/dt normalized” and the fit based upon theory is labeled “withbaseline normalized”. In the presence of the fixed amount of theantagonist, Met, the experimental points are labeled “dP/dt with Metnormalized to Iso” and the fit based upon calculation is labeled “fit toMet normalized”. The last curve displayed is the projected curve for theoptimal composition which is labeled “with f*[Met]/K_(i)”. The K_(DH),K_(DL) and K_(i) were obtained from this fit and put into the finalequation for “f” (the fraction of the dose of the antagonist to use withrespect to the agonist). From the fit, the values obtained wereK_(DH)=19.0; K_(DL)=1.3 and K_(i)=300 micrograms/kg/min. These valueswere substituted into the equation for f, which yielded 85 to thenearest integer as the optimal ratio. For each microgram amount ofisoproterenol, was mixed 85 micrograms of metoprolol and experimentallytested; this is shown in FIG. 9, the graph labeled “Cardiac Response(dP/dt) in Rat”. Therefore, the optimal ratio was 1:85, Iso:Met. This isthe ratio which was used to generate the second curve, labeled “Iso/MetCombination”.

Summary of the Experiments to Test the Combination of Beta-1-Agonistswith Antagonists to Prevent Desensitization

[0080] Background

[0081] Isoproterenol (Isuprel) and dobutamine are two drugs commonlyused today in patients with decreased cardiac output and heart failure.Both are sympathomimetic adrenergic agonists that bind beta-adrenergicreceptors and thus promote increased heart rate and contractility.

[0082] Metoprolol (Lopressor) is conversely a beta-adrenoreceptorblocking agent that selectively blocks the beta-1-receptors and isfrequently prescribed for heart failure.

[0083] The time-derivative of the blood pressure in the ventricle of theheart (dP/dT) is an accepted measurement of the contractility of theheart: as the strength of the contractions in the ventricle of the heartgoes up, the rate at which the pressure in the ventricle rises willincrease. Increased dP/dT therefore implies increased contractility.

[0084] Consequently it was proposed that, by infusing an adrenergicagonist in a specific combination with a beta-1-receptor blocker (seeU.S. Pat. No. 5,597,699 ('699)) and measuring the resultant leftventricular pressure (LVP) and dP/dT, it would be possible to induce andmeasure an increased contractility and cardiac output without sufferinga corresponding increase in desensitization.

[0085] All beta-1-receptor experiments were performed by Gwathmey, Inc.(Boston).

[0086] Hypothesis

[0087] An undesired side effect that accompanies the use of adrenergicagonists Isoproterenol (Isuprel) and dobutamine is desensitization. Inaddition, these drugs also produce an increase in heart rate(tachycardia) and arrhythmias. It was proposed that, if these drugs arecombined and administered in an optimal ratio as calculated by '699,then the desensitization will be markedly diminished or absent. Theagonistic effects of isoproterenol and dobutamine will produce increasedcontractility with a better therapeutic response; a sustainedcontractility and possibly reduced arrhythmogenesis with the combinationdrugs (isoproterenol+metoprolol=Iso+Met or dobutamine+metoprolol=Dob+Met) than with either drug alone (Iso or Dob).

[0088] Methods

[0089] Isoproterenol (Iso) and dobutamine (Dob) were tested in vivo withand without the beta-1-antagonist, metoprolol (Lopressor)(Met).

[0090] For each of the following experiments, a rat weighing from twohundred to three hundred grams was anesthetized by intraperitoneal (IP)injection of 75-mg/kg sodium pentobarbital (Sodium Nembutal). Followingsedation, the neck of the rat was incised and a tracheotomy wasperformed, inserting a 14-gauge angiocatheter sheath into the trachea ofthe rat and securing it with a silk tie. The angiocatheter was connectedthrough a small tube to a small animal respirator supplied with 1.0liters of oxygen per minute and set to 95 breaths per minute.

[0091] The right carotid artery was next tied off, and after making asmall incision, a Micro-Tip Millar pressure catheter was introduced downthrough the carotid artery, placing the end of the catheter into theleft ventricular cavity of the rat's heart. Position of the catheter tipwas determined by the waveform of the pressure reading-placement in theleft ventricle was presumed when a diastolic pressure of zero mmHg and areasonable systolic pressure (70 to 150 mmHg) was observed. Onceproperly placed, the catheter was secured to the artery with 1-0 silkties.

[0092] Following placement of the Millar catheter, the right jugularvein of the rat was tied off and cannulated by incising the side of thevein and introducing a small (0.3 mm internal diameter), 20centimeter-long intracatheter pre-loaded with 0.9% saline solution intothe vein. Once a reasonable length of the catheter was inserted into thevein, it was tied to the vein with 1-0 silk suture to secure it inplace.

[0093] The Millar pressure catheter was then connected through a Millartransducer control unit to a digital/analog recording card in aSonometrics computer. The transmitted Millar pressure signal was thenzeroed and calibrated in the Sonometrics SonoLAB data acquisitionprogram.

[0094] At this point for each rat, a baseline recording was obtained ofthe left ventricular pressure tracing. Segments of three to five secondswere recorded, and it was from these recorded tracings that the includedfigures of maximum left ventricular pressure (reported as LVP), maximumtime-derivative of left ventricular pressure (dP/dT), and heart rate(HR) were later determined, by analysis with Sonometrics CardioSOFT dataanalysis software.

[0095] At this point in the experimentation, the procedure followeddiffered depending upon which drugs and mixtures were being examined, asis described in the following paragraphs.

[0096] The IV line was connected to a syringe of isoproterenol (Isuprel)or dobutamine in solution on a fluid infusion pump. The isoproterenolwas administered at varying rates (see figures); at each rate the LVPtracing was recorded after several minutes at a constant infusion rate,and the tracing was later analyzed in the same manner as described abovefor the baseline LVP recordings. The same procedure was then performedin the rats using a solution of metoprolol alone. Again, at each rate,LVP was recorded for later analysis. The procedure was repeated a thirdtime, except that infusion rate of isoproterenol was varied while at thesame time a constant dosage of metoprolol (1 mg/kg/min) wasadministered. This constant dose is not the calculated ratio, but servedto calculate an accurate K_(i) for metoprolol in these rats.

[0097] In the Iso exposed rats, there were a set of experiments donewhere the rats served as their own controls. In these experiments therats were first given Iso alone to either 20 microgram/kg/min dosages oruntil arrhythmias occurred. They were then allowed to rest and given theIso+Met combination up to either 20 microgram/kg/min dosages or untilarrhythmias occurred. The dP/dt observations were recorded for eachinfusion.

[0098] In rats 1 through 7, dobutamine solution was first infused atvarying rates and LVP tracings were recorded. In these experiments, therats were first infused with a low-concentration solution (for accuracyof administered dosage). After the rate of dobutamine administration hadprogressed ˜50 to 100 times the initial dosage, the solution wasswitched to a high-concentration (ten time as concentrated as thelow-concentration) solution of dobutamine. This was done to avoidover-loading the rats with too much fluid volume. After completion ofthe dobutamine infusion in rats 1 through 7, the rats were then infusedwith a metoprolol solution, at the rates seen in the attached datatables (not shown). LVP was again recorded for later analysis at eachinfusion rate.

[0099] In rats 8 through 11, the rats were infused with the combinationsolution of dobutamine and metoprolol, in the calculated ratio of 1.0 mgdobutamine to 1.6 mg metoprolol. Infusion rates are displayed in theattached data; LVP tracings were taken at each rate. As was done in thestraight dobutamine infusions in rats 1 through 7, the Dob+Metcombination was switched from a low-concentration solution to aten-times more concentrated solution (after the dosage of 100 times theinitial dosage), again to avoid over-loading the rat with fluid volume.

[0100] Upon completion of each experiment, the rats were euthanized byintravenous (IV) overdose of sodium pentobarbital (75 mg/kg).

[0101] Results

[0102] Initially, the data obtained from the rats given isoproterenolalone were fit to the theoretical calculations and are presented in FIG.9. In order to compare these data sets it is routine in pharmacologicalpractice to zero and normalize each set of data to a common baseline sothat the data can be compared and analyzed. As can be seen in the graph(FIG. 9: Iso normalized to baseline), with increasing administration ofIso, the dP/dT increased at low dosages, but peaked and rapidlydecreased at higher dosages (desensitization), at the same timeincreasing the number of arrhythmias produced in the heart. The theoryfit the experimental data very well with reasonable biophysicalparameters (see FIG. 11 in the conclusion).

[0103] These experiments performed initially on the rats were done inorder to determine the biophysical parameters (KDH, KDL and Ki) forcalculating the optimal combination of a beta-1-agonist with antagonistaccording to the patent, '699. Based on these data, the combination of1.0 mg isoproterenol with 18 mg metoprolol was calculated, and thentested in rats 5 through 7. Whereas for the dobutamine tests, thecombination of 1.0 mg dobutamine with 1.6 mg metoprolol was calculated,and then tested in rats 8 through 11.

[0104] Next presented are the data from rats (5-7) tested with thecomposition Iso+Met in the graph in FIG. 9 titled “Cardiac Response(dP/dt) in the Rat” (Iso/Met combination). When the two were combined,it can be seen that the same increase in dP/dT was observed at lowdosages of isoproterenol, but at higher dosages the dP/dT leveled off atan elevated level, rather than decreasing sharply (no desensitizationoccurred with the combination—Iso+Met). As seen in this graph (FIG. 9),the Iso+Met combination showed a better therapeutic response with asustained response into the range of concentrations wheredesensitization would have normally occurred. In addition, there weremuch less arrhythmias observed in the Iso+Met run than in the Iso alonerun.

[0105] Next presented are the data from the rats (4-7) treated withdobutamine alone (Dob), in which first dobutamine and then metoprololalone were administered. Similar to the effects observed with theisoproterenol administration, it can be seen in the graph (FIG. 10:(Dob)) that at low dosages of dobutamine, the dP/dT increased; howeverat higher dosages the dP/dT again began to decrease (desensitization).With administration of metoprolol alone, there was observed a steadilylarger decrease in dP/dT with every increasing dosage administered (notshown). In these seven rats, LVP was also recorded for each rat, and thegraphs (not shown) show an effect in LVP parallel to the respectiveeffects in dP/dT with administration of dobutamine or metoprolol alone.Administration of metoprolol alone served as a control to demonstratethat the metoprolol was acting as a β-1 antagonist in these animals.

[0106] In rats eight through twelve, the calculated combination of 1.0mg dobutamine to 1.6 mg metoprolol was administered. Although these ratswere given final dosages as high as 8,000 micrograms/kg/min andcumulative dosages estimated to be as high as 70,000 to 90,000micrograms/kg, they functioned relatively well up until dosages past1,000 micrograms/kg/min or estimated cumulative dosages of about 10,000to 20,000 micrograms/kg. At the highest dosages past 1,000micrograms/kg/min, dP/dt, LVP and heart rate (HR) all declined.

[0107] There were several possible reasons for the decrease in heartcontractility at these extremely high dosages. First, the toxic levelreported for the dobutamine LD50 i.v. in mice is 73 mg/kg (Merck Indexp. 3453 (1996)); therefore, the rats were within this range where thetoxic effects of dobutamine overwhelm any therapeutic effects and leadto the decline in the viability of the animals. Second, the problem withexcessive fluid administration is problematic in these small animals;leading to electrolyte abnormalities and cardiac arrhythmias on thebasis of too much fluid within the cardiovascular system. Given thesecaveats, the data for the Dob+Met rats were taken up to the 1,000microgram/kg/min dosages and compared to the Dob only rats that weregiven dosages up to 800 microgram/kg/min.

[0108] Taking each set of data zeroing to a baseline and normalizing sothat the data can be compared, is routine in pharmacological practice.The normalized averages for each set were compared in FIG. 3 below. Forthe Dob+Met group it can be seen that the response was maintainedthroughout the range; whereas, the Dob group showed a decline inresponse (see FIG. 10). As can be seen in FIG. 10, as the rate ofadministration of Dob was increased, dP/dT first increased, then peaked,and began to decrease at high dosages (desensitization). A similareffect was observed in the LVP-first an increase, a peak, a slightdecrease that leveled off and finally a continued decrease at extremelyhigh dosages. It is important to note however that the peaks in thedP/dT and LVP graphs do not correlate: in fact, the peak in the dP/dTgraph came at a point when the LVP levels had returned to baseline. Thegraph of heart rate versus infusion rate shows that heart rate remainedconstant until extremely high levels of infusion, at which point theheart rate began to decrease swiftly which could have been due to thetoxic effects of the drug at these high dosages.

[0109] Conclusions

[0110] When considering the raw data representing the isoproterenoltests, one can see that while infusing the combination of Iso+Met mayhave slightly diminished the absolute action of increasing dP/dT, thepercentage change in dP/dT from baseline was largely matched by thismixture. One can also see that while high doses of pure isoproterenolresulted in a decreased dP/dT (desensitization), dP/dT duringadministration of the combination Iso+Met leveled off at an elevatedlevel (no desensitization) which was sustained into the higher dosageswhere desensitization would normally occur. This effect suggests promisefor the possibility of administering dosages of isoproterenol withouthaving to worry about a dramatic decrease in the contractility of theheart or the potentially fatal increase in cardiac arrhythmias.

[0111] From these graphs (see FIGS. 9 and 10), one can see that thecombinations Iso+Met or Dob+Met quickly increased dP/dT at low dosages,before stabilizing it at higher dosages. While LVP was first increasedat low dosages, it stabilized at baseline levels for the higher dosages.Heart rate remained largely unaffected. These results are exciting inthat they suggest that if the right combination of dobutamine andmetoprolol is administered, it may indeed be possible to increase dP/dT(i.e. contractility, and thus cardiac output) without affecting theblood pressure or heart rate in the patient. In all, these experimentspresent exciting prospects for the hope of improving cardiac outputwithout drug desensitization, arrhythmogenesis or tachycardia.

[0112] At the higher drug concentrations, there may occur a number ofeffects that include toxicity; excess fluid administration andelectrolyte abnormalities. Although there was no mention made ofarrhythmias, these rats appeared to maintain a very high output levelover a long time. Although further testing should be done, it appearsthat these experiments support the hypothesis that desensitization canbe reduced or eliminated in the β-1 agonist drugs by combining a β-1antagonist with the agonist in the proper ratio to allow these drugs toincrease contractility of the heart with a better therapeutic response;a more sustainable response and less cardiac arrhythmias.

[0113] Finally in considering the ability of the theory from '699 to fitthe experimental data, there were essentially three tests of the theoryin these experiments. First, the theory was used to fit the initialexperimental observations with Iso or Dob alone; Met alone and a fixedamount of Met with Iso or Dob. Second, the biophysical parametersderived from the initial fit (K_(DH), K_(DL) and K_(i)) were used tocalculate a specific ratio as given in '699. Third, the experiments wereconducted with and without the calculated combination and theobservations were examined for their fit to the expected values. As seenin FIG. 11, the theory (Δ) fit the experimental data very well.

[0114] The administration of antagonist is by normal delivery methods ofits own character and may be done during the agonist administration or,if such is autonomic in the recipient, concurrent therewith, or shortlythereafter. It is also well known that agonists and antagonist can bemade into pharmaceutical compositions by combinations with appropriatemedical carriers or diluents. For example, such mixtures can bedissolved in oils, propylene glycol, physiological saline, isopropylmyristate, ethanol, cremophor, glycol, sesame oil, or other suchpharmacological solutions. Formulation as topicals is also available.Pharmacologists familiar with the panoply of drugs and theirprofessional literature may readily use the invention with the guidanceherein provided.

[0115] This more physiologically subjective (and practical) method, andthe compositions derived thereby, constitute effective and significantimprovements to my original work. They are commended to the fieldconsistent with the hereinafter appended claims.

What is claimed is:
 1. A formulation containing an optimally effectiveratio of an antagonist mixed with an agonist to prevent desensitizationof agonist-specific cell receptors and concomitantly maintain maximumresponse to the agonist, comprising: a first amount of agonist-ligandeffective for acquiring a desired, specific response from saidreceptors; and a second amount of antagonist-ligand, to maximize andsustain said response, wherein the second amount is from about 10⁺⁶ toabout 10⁻⁶ of said first amount.
 2. The formulation of claim 1 whereinthe antagonist and the agonist form a defined antagonist/agonist pairingspecific to and within a cellular receptor class.
 3. The formulation ofclaim 2 wherein an antagonist/agonist pairing is selected from the groupconsisting of propranolol/isoproterenol; atenolol/norepinephrine ;metoprolol/dobutamine; timolol/ephedrine; 2-amino-5-pphospho-nopentanoic acid/N-methyl-D-aspartic acid;progesterone/oxytocin; sotalol/epinephrine; pindolol/noradrenaline;betaxolol/xamoterol; and propanolol/terbutaline.
 4. The formulation ofclaim 2 wherein the pairing further comprises an enantiomer of abeta-1-antagonist and a beta-1-agonist.
 5. A formulation that elicits adesired response from cellular receptors and prevents subsequentdesensitization of said receptors comprising an agonist suitable foreliciting said response in a first amount effective for binding to saidreceptors in both a high and a low affinity state effective forobtaining said response mixed with an inhibitor of said agonist specificto said receptors, said inhibitor in a second amount sufficient toprevent desensitization of said receptor, said second amount beingK_(i)(K_(DL)K_(DH)/²)^(½)where K_(DL) and K_(DH) are dissociationconstants of said agonist-ligand, and K_(i) is the dissociation constantof said antagonist-ligand.
 6. The formulation of claim 5 , wherein saidinhibitor is selected from the group consisting of partial antagonists,antagonists and competitive antagonists to said agonist.
 7. Aformulation that elicits a desired response from a cellular receptorwhile preventing subsequent desensitization of said receptor andconsisting essentially of: a first amount of an agonist ligand effectivefor eliciting said response and suitable for ligand binding to saidreceptor to both high and low affinity states; and a second amount of anantagonist ligand, from about 10⁺⁶ to about 10⁻⁶ of the first amount,effective for maximizing said response and preventing desensitization ofsaid receptor to the agonist ligand by binding partially in said secondamount to said receptor substantially in said high affinity state tocompete with the agonist ligand for said both states.
 8. The formulationof claim 7 , where said second amount is K_(i)(K_(DL)K_(DH)/2)^(−½)thefirst amount, where K_(DL) and K_(DH) are dissociation constants of saidagonist-ligand, and K_(i) is the dissociation constant of saidantagonist-ligand.
 9. A formulation containing an optimal ratio of anantagonist mixed with an agonist for preventing desensitization ofagonist-specific cell receptors and maximizing response by saidreceptors comprising: a first amount of agonist effective for acquiringa desired response from said receptors; and a second amount ofantagonist effective for inhibiting said response, said second amount ina ratio from about 10⁺⁶ to about 10⁻⁶ of said first amount of theagonist, said second amount being in a ratio to the first amount of thedissociation constant of said antagonist divided by the square root ofhalf the product of high affinity and low affinity dissociationconstants of said agonist.
 10. The formulation of claim 9 , wherein saidantagonist is selected from the group consisting of partial antagonists,antagonists and competitive antagonists to said agonist.
 11. Aformulation that elicits a desired optimal response from a cellularreceptor while preventing subsequent desensitization of said receptorand consisting essentially of: a first amount of an agonist-ligandeffective for eliciting said response and suitable for ligand binding tosaid receptor to both high and low affinity states; and a second amountof an antagonist-ligand, from about 10⁺⁶ to about 10⁻⁶ of the firstamount, effective for maximizing said response and preventingdesensitization of said receptor to the agonist-ligand by bindingpartially in said second amount to said receptor substantially in saidhigh affinity state to compete with the agonist-ligand for said bothstates.
 12. The formulation of claim 11 , where said second amount isK_(i)(K_(DL)K_(DH)/2)^(−½)the first amount, where K_(DL) and K_(DH) aredissociation constants of said agonist-ligand, and K_(i) is thedissociation constant of said antagonist-ligand.
 13. The formulation ofclaim 12 wherein an antagonist-/agonist-ligand combination is selectedfrom the group consisting of propranolol/isoproterenol;atenolol/norepinephrine; metoprolol/dobutamine; timolol/ephedrine;2-amino-5-p phospho-nopentanoic acid/N-methyl-D-aspartic acid;progesterone/oxytocin; sotalol/epinephrine; pindolol/noradrenaline;betaxolol/xamoterol; and propanolol/terbutaline.
 14. The formulation ofclaim 12 further comprising an enantiomer of a β-1 antagonist and a β-1agonist.
 15. The formulation of claim 12 wherein an antagonist-/agonist-ligand combination is selected from the group consisting ofpropranolol/isoproterenol; atenolol/isoproterenol;betaxolol/isoproterenol; metoprolol/isoproterenol;timolol/isoproterenol; sotalol/isoproterenol; pindolol/isoproterenol;betaxolol/isoproterenol; propranolol/epinephrine; atenolol/epinephrine;betaxolol/epinephrine; metoprolol/epinephrine;timolol/epinephrine;sotalol/epinephrine; pindolol/epinephrine; betaxolol/epinephrine;propranolol/terbutaline; atenolol/terbutaline; betaxolol/terbutaline;metoprolol/terbutaline; timolol/terbutaline; sotalol/terbutaline;pindolol/terbutaline; betaxolol terbutaline; propranolol/norepinephrine;atenolol/norepinephrine; betaxolol/norepinephrine;metoprolol/norepinephrine; timolol/norepinephrine;sotalol/norepinephrine; pindolol/norepinephrine;betaxolol/norepinephrine propranolol/dobutamine; atenolol/dobutaminebetaxolol/dobutamine; metoprolol/dobutamine; timolol/dobutamine;sotalol/dobutamine; pindolol/dobutamine; betaxolol/dobutaminepropranolol/ephedrine; atenolol/ephedrine; betaxolol/ephedrine;metoprolol/ephedrine; timolol/ephedrine; sotalol/ephedrine;pindolol/ephedrine; betaxolol/ephedrine propranolol/xamoterol;atenolol/xamoterol; betaxolol/xamoterol; metoprolol/xamoterol;timolol/xamoterol; sotalol/xamoterol; pindolol/xamoterol; andbetaxolol/xamoterol.
 16. The formulation of claim 12 wherein thecombination further comprises enantiomers of the β-2 antagonists or β-1antagonists and β-1 agonists or β-2 agonists.